Topological Modal Logic for Subset Frames with Finite Descent
We slightly modify the semantics of Moss' and Parikh's topological modal language ([MP]). This enables us to study the topological modal theory of further classes of subset spaces. Subsequently we deal in particular with spaces where every chain of opens is finite. We axiomatize the logic of those quasi-finite spaces, and prove soundness und semantical completeness of the proposed set of axioms. Moreover, it turns out that one can decide whether a given formula is a theorem of that logic. We also handle a somewhat wider dass of subset spaces, which satisfy a more general finite-descent-condition on the set of opens.
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